How to add a face connecting two meshes
I suggest another approach. It needs some calculation at the beginning to handle correctly where the holes are to be placed, but it does so your final shape has no 'ngons' (faces with more than 4 vertices) which is always better.

The principle is to start with a plane, and give it some symmetrical loop cuts in order to place the future holes :



Now we want to make one hole (this one will be duplicated after that) :


Select a place for the future hole
Inset I and move the mouse to scale/place the inset faces
Select the outer vertices and make them circular AltShiftS 
Scale a bit to adjust





Now extrude E the inner part 




Add a subdivision surface modifier to check the result and eventually refine it (add some bevel for instance, if needed).



Once done, all is matter of duplicating the hole and merge the six faces.

Make each die's face by duplicating the initial hole :


Delete a vertex to make a place for the hole
Select the hole
Set the snapping mode to vertex
Duplicate the hole and place it
Once done, select all and remove doubles




Do that for the six faces and reassembly all in a complete die :